The Annals of Statistics

On image segmentation using information theoretic criteria

Alexander Aue and Thomas C. M. Lee

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Image segmentation is a long-studied and important problem in image processing. Different solutions have been proposed, many of which follow the information theoretic paradigm. While these information theoretic segmentation methods often produce excellent empirical results, their theoretical properties are still largely unknown. The main goal of this paper is to conduct a rigorous theoretical study into the statistical consistency properties of such methods. To be more specific, this paper investigates if these methods can accurately recover the true number of segments together with their true boundaries in the image as the number of pixels tends to infinity. Our theoretical results show that both the Bayesian information criterion (BIC) and the minimum description length (MDL) principle can be applied to derive statistically consistent segmentation methods, while the same is not true for the Akaike information criterion (AIC). Numerical experiments were conducted to illustrate and support our theoretical findings.

Article information

Ann. Statist. Volume 39, Number 6 (2011), 2912-2935.

First available in Project Euclid: 24 January 2012

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 62P30: Applications in engineering and industry 62H35: Image analysis
Secondary: 62G05: Estimation

Akaike information criterion (AIC) Bayesian information criterion (BIC) image modeling minimum description length (MDL) piecewise constant function modeling statistical consistency


Aue, Alexander; Lee, Thomas C. M. On image segmentation using information theoretic criteria. Ann. Statist. 39 (2011), no. 6, 2912--2935. doi:10.1214/11-AOS925.

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